ACR X UNAUTH DSCNT FROM ASSIGNED ALT HAD LTSS WITH ACFT AT 4000 FT.

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AZO APCH THEN CLRED ACR X TO 7000 FT; 290 DEG HDG; AND CALL THE FIELD IN SIGHT FOR VISUAL TO RWY 17. WE REQUESTED RWY 35 (WINDS CALM) AS IT WAS SHORTER TIME INVOLVED; BUT WERE TOLD NEGATIVE. SO WE COMPLIED WITH 7000 FT 290 DEGS. APCH 5 MI S OF BTL; WE CALLED FIELD IN SIGHT. AZO APCH THEN SAID 'ROGER; AND KEEP YOUR SPD 250 KTS OR GREATER UNTIL 10 DME.' THAT CAUSED SOME CONFUSION IN COCKPIT BUT REPLIED '250 OR GREATER TILL 10 DME.' WE BOTH THOUGHT WE HAD BEEN CLRED VISUAL AND STARTED A SHALLOW DSCNT OUT OF 7000 FT. TURNED L TO A MORE WESTERLY HDG FOR L BASE RWY 17 AT AZO. AT APPROX 4700 FT; AZO APCH CALLED AND SAID 'CLRED TO 5000 FT. WE BOTH FROZE; LOOKED AT EACH OTHER; THEN REPLIED '5000 FT. WE THOUGHT WE WERE CLRED VISUAL?' AZO APCH SAID; 'NEGATIVE CLB TO 5000 FT AND MAINTAIN 290 DEG HDG;' AND THEN AZO. APCH SAID 'DIDN'T YOU SEE THAT TFC GO BEHIND YOU AT 4000 FT.' WE SAID 'WHAT TFC; NEGATIVE!' (THIS WAS THE FIRST MENTION OF ANY TFC; LET ALONE ANY POSSIBLE CONFLICT; BY AZO APCH). 'WE SAID WE HAD THE FIELD IN SIGHT AND WE THOUGHT YOU CLRED US FOR THE VISUAL.' AZO APCH THEN REPLIED; NEGATIVE; I NEVER CLRED YOU FOR THE VISUAL. YOU MAY HAVE HAD BTL IN SIGHT BUT YOU DIDN'T HAVE AZO IN SIGHT.' (THE VISIBILITY WAS RPTED ON ATIS AS 15 MI; BUT IT WAS AT LEAST 25-30 MI AT OUR ALT.) AZO APCH CTL THEN SAID 'YOU'D BETTER CALL TWR WHEN YOU LAND AND TALK TO THE SUPVR. CONTRIBUTING: SHORT FLT COCKPIT WORKLOAD WAS EXTREMELY BUY (CTL OF PRIMARY VHF COM RADIO CONSTANTLY PASSED BACK AND FORTH) PRE-OCCUPATION ON USE OF NON-STANDARD CLRNCS (IE; 250 KTS OR GREATER BELOW 10000 FT MSL.) COMPLACENCY ON PART OF PLTS HEARING ONLY WHAT WE THINK WE WANT TO HEAR. SUPPLEMENTAL INFO FROM ACN 298121: WE WERE TOLD TO RPT THE ARPT IN SIGHT FOR A VISUAL APCH. WE REPLIED 'ARPT IN SIGHT.' THE APCH CTLR RESPONDED AND SAID 'MAINTAIN 250 KTS OR GREATER UNTIL 10 DME.' TCASII MEL: HAD TCASII NOT BEEN DEFERRED; WE WOULD HAVE HAD A HEADS UP ON THIS TFC. POSSIBLE COMPLACENCY ON PART OF CTLR AND PLTS. GREAT WX. NOT TOO BUSY ARPT. THE PROB WAS DISCOVERED WHEN APCH CTL ISSUED US A CLRNC TO 5000 FT. AT THAT POINT WE WERE AT 4700 FT; 2300 FT BELOW OUR LAST ASSIGNED ALT.